Bayesian models have become very popular over the
last years in several fields such as signal processing, statistics and machine learning. Bayesian inference needs the approximation of complicated integrals involving the posterior distribution. For this purpose, Monte Carlo (MC) methods, such as Markov Chain Monte Carlo (MCMC) and Importance Sampling (IS) algorithms, are often employed. In this work, we introduce theory and practice of a Compressed MC (C-MC) scheme, in order to compress the information contained in a could of samples. CMC is particularly useful in a distributed Bayesian inference framework, when cheap and fast communications with a central processor are required. In its basic version, C-MC is strictly related to the stratification technique, a well-known method used for variance reduction purposes. Deterministic C-MC schemes are also presented, which provide very good performance. The compression problem is strictly related to moment matching approach applied in different filtering methods, often known as Gaussian quadrature rules or sigma-point methods. The connections to herding algorithms and quasi-Monte Carlo perspective are also discussed. Numerical results confirm the benefit of the introduced schemes, outperforming the corresponding benchmark methods.
In this paper, asymptotic expansions of the distributions and densities of powered extremes for Maxwell samples are considered. The results show that the convergence speeds of normalized partial maxima relies on the powered index. Additionally, compared with previous result, the convergence rate of the distribution of powered extreme from Maxwell samples is faster than that of its extreme. Finally, numerical analysis is conducted to illustrate our findings.
Authors: Ilija Barukčić
Comments: 31 pages. Copyright © 2018 by Ilija Barukčić, Jever, Germany. All rights reserved. Published by
Background: Human papillomavirus (HPV) has an important role in the oncogenesis of several malignant diseases. Some observational studies demonstrated the presence of HPV even in human prostate cancer (PC) while other studies failed on this point. The relationship between HPV infection and PC remains unclear. The aim of the present meta-analysis study is to investigate whether HPV serves as a cause or as the cause of PC.
Methods: The PubMed database was searched for suitable articles. Previously published expert reviews and systematic meta-analysis were used as an additional source to identify appropriate articles. Articles selected for this meta-analysis should fulfill the following inclusion criteria: (a) no data access barrier, (b) polymerase chain reaction (PCR) DNA based identification of HPV. The method of the conditio sine qua non relationship was used to prove the hypotheses whether being married is a necessary condition (a conditio sine qua non) of PC. In other words, without being married no PC. The method of the conditio per quam relationship (sufficient condition) was used to prove the hypotheses if HPV is present in human prostate tissues then PC is present too. The mathematical formula of the causal relationship k was used to prove the hypothesis, whether there is a cause effect relationship between HPV and PC. Significance was indicated by a p-value (two sided) of less than 0.05.
Results: In toto more than 136 000 000 cases and controls were re-analysed while more than 33 studies were considered for a meta-analysis. Several studies support the hypotheses without being married no PC. All the studies considered for a re-analyses support the null-hypotheses if HPV then PC, while the cause effect relationship between HPV and PC was highly significant.
Conclusions: Human papillomavirus is the cause of human prostate cancer.
In this research, we present neutrosophic decision-making, which is an extension of the classical decision-making process by expanding the data to cover the non-specific cases ignored by the classical logic, which in fact support the decision-making problem. The lack of information besides its inaccuracy is an important constraint affecting The effectiveness of the decision-making process, and we will rely on the decision tree model, which is one of the most powerful mathematical methods used to analyze many decisionmaking problems, where we extend it according to the neutrosophic logic by adding some indeterminate data (in the absence of probability) or by substituting the classical probabilities with the neutrosophic probabilities (in case of probability). We call this extended model the neutrosophic decision tree, which results in its use to reach the best decision among the available alternatives because it is based on data that is more general and accurate than the classical model.